Let H be a finite dimensional semisimple Hopf algebra over a field and A an H-module algebra. In this paper, we characterize any H-separable Galois extension of an Azumaya algebra. Assuming that A/AH is an H-separable...Let H be a finite dimensional semisimple Hopf algebra over a field and A an H-module algebra. In this paper, we characterize any H-separable Galois extension of an Azumaya algebra. Assuming that A/AH is an H-separable extension, we prove that A/AH is H-Galois and AH is Azumaya if and only if A#H is an Azumaya Z-algebra, where Z is the center of A#H(not necessarily C(A)H).展开更多
Let H be a finite dimensional Hopf algebra over a field and A an H-module algebra. The H induces an action on the CA#H(A) by adjoint and CA#H(A)H= Z(A # H) = C,where CA#H(A) denotes the centralizer which algebra A in ...Let H be a finite dimensional Hopf algebra over a field and A an H-module algebra. The H induces an action on the CA#H(A) by adjoint and CA#H(A)H= Z(A # H) = C,where CA#H(A) denotes the centralizer which algebra A in A # H and Z(A # H) the center of A # H.The aim of this paper is to discuss ,the Galois conditions on the centralizer CA# H(A).We prove that CA# H(A)/ZA # H is H* -Galois if and only if CA# H(A)# H/CA# H(A) is H-separable). Furthermore , if H is a finite dimensional semisimple Hopf algebra and CA# H(A)# H is an Azumaya C-algebra or A # H/A is H-separable, CA# H(A) satisfies the double centralizer property in CA# H(A)# H, CA# H(A)/C is separable and there exists a cocommutative left integral t ∈∫1H,then CA# H(A)/C is H*-Galois.展开更多
基金The NSF (19771046) of China and Anhui Province Education Committee Fund (99jl0209).
文摘Let H be a finite dimensional semisimple Hopf algebra over a field and A an H-module algebra. In this paper, we characterize any H-separable Galois extension of an Azumaya algebra. Assuming that A/AH is an H-separable extension, we prove that A/AH is H-Galois and AH is Azumaya if and only if A#H is an Azumaya Z-algebra, where Z is the center of A#H(not necessarily C(A)H).
文摘Let H be a finite dimensional Hopf algebra over a field and A an H-module algebra. The H induces an action on the CA#H(A) by adjoint and CA#H(A)H= Z(A # H) = C,where CA#H(A) denotes the centralizer which algebra A in A # H and Z(A # H) the center of A # H.The aim of this paper is to discuss ,the Galois conditions on the centralizer CA# H(A).We prove that CA# H(A)/ZA # H is H* -Galois if and only if CA# H(A)# H/CA# H(A) is H-separable). Furthermore , if H is a finite dimensional semisimple Hopf algebra and CA# H(A)# H is an Azumaya C-algebra or A # H/A is H-separable, CA# H(A) satisfies the double centralizer property in CA# H(A)# H, CA# H(A)/C is separable and there exists a cocommutative left integral t ∈∫1H,then CA# H(A)/C is H*-Galois.
